Sun-Earth-Moon Gravity

The natural state of a piece of matter is to trace out a straight path through space-time, known as a geodesic. Because space-time is curved, these straight paths appear curved from our limited 3d viewpoint. Examples of the these straight paths are a stone dropped down a shaft which has been evacuated of air, the moon's orbit around the Earth, the Earth's orbit around the Sun, etc.For most models of the Universe, there is no centre of gravity as there is no centre...

Really? Oh thank God. You may just have saved the tens of thousands of professional cosmologists/particle physicists/relativists from wasting their lives on a useless pursuit. Have you written to all of the relevant departments yet? They will be overjoyed to hear from you! You're so right. All my time as a professional scientist was spent unwittingly making this very same error, but now you put it this way it is so easy for me to see the complete folly behind my approach.

Ok, first off has little to no relevance in science.You then follow your "personal opinion" with That's a mighty big conclusion to draw from your own personal opinion. It may well be true, but it hardly follows... The error was in Believe me, none of us think like that (although a couple did back around 1980 with N=8 SUGRA, but they shall remain nameless) Of course there are problems. And of course there will be modifications and new models. But to direct the level of tentativity you did at the most basic elements of GR is naive. If I had been explaining the ways in which string theory can remove the singluarities of GR, or even how cold dark matter factors into the large scale structure of the universe, you would have a point. But we are talking about the most accurately tested theory known to man, a theory that is over 90 years old. It will require a bit more than anyone's "personal opinion" to budge. Not at all. I'm just very defensive about my life's passion. Just remember, what I described is not some new-fangled hyper-theoretical super-jargon - it is exactly as it would have been explained in 1915... except they wouldn't have had the luxury of ninety years of solid evidence to back them up!